Syrian refugees at the Za'atri refugee camp in Mafraq, Jordan - about 1,000 a day continue to arrive from Syria. Photograph: Majed Jaber/Reuters

The UN refugee agency has reported a dramatic increase in the number of people fleeing the violence in Syria after more than 100,000 people sought asylum in neighbouring countries during August.

This brings the total number of Syrian refugees registered or awaiting registration to more than 235,300.

The UNHCR's chief spokeswoman, Melissa Fleming, said the exit of 103,416 Syrians last month was "a significant escalation in refugee movement and people seeking asylum, and probably points to a very precarious and violent situation inside the country".

As a result, UN agencies are likely to face pressure to revise their $193m (£122m) estimate of the cost of helping the refugees this year. That figure – in June – was based on expectations that there would be 185,000 refugees from Syria by the end of 2012.

Among neighbouring countries, Iraq has seen a significant increase in the number of Syrian Kurds arriving in the past week, with an estimated 500 Syrians crossing each day, compared with 500 a week in the first three weeks of August, the UNHCR says.

In Jordan, where there are already more than 77,000 refugees, Syrians continue to arrive at a rate of about 1,000 a day. The Jordanian government and relief agencies are making preparations for as many as 150,000 people.

There are more than 80,000 refugees in Turkey where the UNHCR says the Turkish government is making plans to handle at least 150,000 refugees if the conflict keeps worsening.

In Lebanon, there are more than 59,000 displaced Syrians who are registered or are awaiting registration. This week the UNHCR is opening a mobile registration centre in Baalbek in the eastern Bekaa valley in response to the increasing number of displaced Syrians who are arriving in the area.

On Tuesday, Peter Maurer, head of the International Committee of the Red Cross, met the Syrian president, Bashar al-Assad, in Damascus.

According to the ICRC, Assad gave a positive reaction to plans to expand humanitarian operations in Syria. Maurer stressed the need for improved access to healthcare, and to speed up imports of medical supplies, food and equipment.

However, Syria's state-run news agency, Sana, suggested Assad had showed some scepticism about the international organisation's neutrality. It said Assad "welcomes Red Cross humanitarian operations in Syria as long as it works independently and neutrally".

Sana also claimed that Maurer had "expressed his appreciation for the co-operation shown by the Syrian government, praising the bridges of trust that have been built between the parties".

In other developments on Tuesday, Germany's foreign minister, Guido Westerwelle, called on Syria's disparate Syrian opposition groups to unite in preparation for the collapse of the Assad regime.

Westerwelle said a common platform was urgently needed, and that the people of Syria must see "there is a credible alternative to the regime". He called on the opposition "to create as fast as possible the conditions for … a transition government."

Meanwhile, Abdel Basset Sayda, the head of the opposition Syrian National Council, called for a post-Assad economic recovery plan.

"In the aftermath of the destruction … we are convinced Syria needs a Marshall-style plan to ensure it stands again on solid financial and economic ground," Sayda said in Berlin.

"Without real comprehensive development we will open up the opportunity for the growth of all kinds of extremism in the region," he said.